A Homotopy Method For Stabilization Of Multivariable Systems With Structural Constraints On State Feedback

Various structural constraints on the state feedback gain matrix, K, used in the control of a multivariable dynamical system arise because of the way feedback is realized. Static output feedback, decentralized state feedback, simultaneously stabilizing state feedb, ack for several operating points of a, system, and two-controller feedback are some examples of control structure realizations which impose constraints on K. We cast each of the problems in a general class of problems of stabilizaLion of multivariable systems with such structural constraints into a problem of solving a system of equalities and inequalities which is then solved using a continuous realization of the gradient projection method and a barrier method under the homotopy framework. Our method is illustrated with two examples.